Finite Group Databasebeta

(C3×C241⋊C3)⋊C9 #34086007

order19521
automorphism?
homologyAbelianization (H1) = C3×C9 · Schur multiplier (H2) = C32

Aliases

unambiguous semidirect product(C3×C241⋊C3)⋊C9

Splittings

FittingC3×C9×C241 ⋊ C3
SylowC241 ⋊ C32⋊C9

Subgroups

subgroupG/H
center, FrattiniC32C3×C241⋊C3
commutatorC3×C241C3×C9
FittingC3×C9×C241C3
socle, cosocleC32×C241C32
prime radicalC32×C241⋊C3C3
hypercenterC3×C9C241⋊C3
hypocenterC241C32⋊C9
LCSG ▷ C3×C241 ▷ C241
UCSC1 ◁ C32 ◁ C3×C9

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6507

Polycyclic presentation:

3^4,241|a^3=d,b^a=bc,e^b=e^15

Conjugacy classes & character table

2193 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19521, 18);